Selection and obstruction for mass textures in finite spectral triples with a weight grading

We equip the finite spectral triple of the Standard Model with an external grading by the sixteen spinor weights of B4, decomposed under B2×D2. For mass matrices of the associated Dirac operator we prove:(i) the first‑order condition forces the support onto an explicit weight bijection and imposes no constraint on mass values;(ii) an order‑zero filter (hypercharge conservation) admits only two of sixteen root‑ladder directions into any horizontal extension of the algebra;(iii) the first‑order condition is blind, as a left‑index operator, to every horizontal generator;(iv) repackaging the grading as right indices, the order‑zero window contains no selection point—the unique relation‑producing operator forces an unphysical doublet mass degeneracy;(v) the spectrum is nevertheless realizable: any spectral function of the weight Cartan defines an explicit Dirac operator satisfying all axioms.The conclusion, stated precisely: realizable, not derivable.